Optimal. Leaf size=16 \[ 3+x-\frac {x^2 (5+3 x)}{e^2} \]
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Rubi [A]
time = 0.00, antiderivative size = 18, normalized size of antiderivative = 1.12, number of steps
used = 2, number of rules used = 1, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12}
\begin {gather*} -\frac {3 x^3}{e^2}-\frac {5 x^2}{e^2}+x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (e^2-10 x-9 x^2\right ) \, dx}{e^2}\\ &=x-\frac {5 x^2}{e^2}-\frac {3 x^3}{e^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 18, normalized size = 1.12 \begin {gather*} x-\frac {5 x^2}{e^2}-\frac {3 x^3}{e^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.32, size = 21, normalized size = 1.31
method | result | size |
risch | \(x -5 \,{\mathrm e}^{-2} x^{2}-3 \,{\mathrm e}^{-2} x^{3}\) | \(17\) |
gosper | \(x \left (-3 x^{2}+{\mathrm e}^{2}-5 x \right ) {\mathrm e}^{-2}\) | \(18\) |
default | \(\left (-3 x^{3}-5 x^{2}+{\mathrm e}^{2} x \right ) {\mathrm e}^{-2}\) | \(21\) |
norman | \(x -5 \,{\mathrm e}^{-2} x^{2}-3 \,{\mathrm e}^{-2} x^{3}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 20, normalized size = 1.25 \begin {gather*} -{\left (3 \, x^{3} + 5 \, x^{2} - x e^{2}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 20, normalized size = 1.25 \begin {gather*} -{\left (3 \, x^{3} + 5 \, x^{2} - x e^{2}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 17, normalized size = 1.06 \begin {gather*} - \frac {3 x^{3}}{e^{2}} - \frac {5 x^{2}}{e^{2}} + x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 20, normalized size = 1.25 \begin {gather*} -{\left (3 \, x^{3} + 5 \, x^{2} - x e^{2}\right )} e^{\left (-2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 18, normalized size = 1.12 \begin {gather*} -x\,{\mathrm {e}}^{-2}\,\left (3\,x^2+5\,x-{\mathrm {e}}^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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